CN106684854A - Voltage off-limit risk analysis method of active power distribution network based on node equivalency - Google Patents

Abstract

The invention provides a voltage off-limit risk analysis method of an active power distribution network based on node equivalency. The method comprises the following steps that an equivalent state model of the active power distribution network is established; the voltage off-limit possibilities of different equivalent nodes in the discrete state are calculated; and the voltage off-limit possibility in the practical operation state of a node load is calculated. The characteristics that simplified nodes include fewer equivalent state parameters and an integrated influence of different operation states of the system on the node voltage can be represented are used, discrete states of the equivalent nodes in the active power distribution network can be selected according to node characteristics to carry out offline calculation and generate a corresponding database, and a reference calculation sample is provided for online rapid analysis; problems in rapidly and accurately calculating the node off-limit probabilities of the different nodes of the active power distribution network in practical operation are solved effectively; and the method is helpful for rapid online analysis and calculation, and has a higher accuracy.

Description

Active power distribution network voltage out-of-limit risk analysis method based on node equivalence

Technical Field

The invention relates to an analysis method, in particular to an active power distribution network voltage out-of-limit risk analysis method based on node equivalence.

Background

With the increasing aggravation of energy and environmental problems, new energy and renewable energy power generation technologies are rapidly developed, and distributed power generation technologies which promote the utilization of renewable energy and effectively supplement centralized power generation are also widely applied. As an important representative of a distributed power generation technology, in an active power distribution network, a photovoltaic power generation system is developed most prominently with the advantages of small scale, easy installation, flexible dispersion, clean energy and the like. However, as the permeability of the photovoltaic system is continuously increased, the photovoltaic system is greatly influenced by the environment, and the power output has strong randomness and fluctuation, so that a series of power quality problems are brought to users. In particular, high permeability photovoltaic systems may cause overvoltage conditions in active power distribution networks, making voltage out-of-limit risks more prominent and complex.

For an active power distribution network containing double uncertain factors of load and photovoltaic power generation, voltage out-of-limit risk analysis and calculation are carried out on the active power distribution network, a deterministic calculation problem is converted into a stochastic calculation problem, and probability load flow replaces traditional deterministic load flow calculation to complete analysis and calculation of an uncertain model. The method fully considers the power probability model characteristics of the load and the photovoltaic system, and can represent the integral morphological characteristics of the voltage on possible values compared with discrete values corresponding to specific points of a deterministic model. The method for solving the probability trend mainly comprises a simulation method, an analytic method and an approximation method. The simulation method simulates various uncertain factors and combinations thereof through a large number of samples, theoretically, an accurate nonlinear power flow calculation method can be used, and the correlation among the uncertain factors can be considered, so that the limitation of calculation accuracy is minimum. However, the method has the problems of overlarge calculation amount, long time consumption and the like, and the application of the method in actual operation is restricted. The analytical method requires a large number of convolution operations based on approximate linearization. The approximation method can directly obtain the probability statistical characteristics of the objective function, but certain errors exist in the types of probability distribution outside the normal probability distribution.

If the node loads and the multi-dimensional uncertain models of the photovoltaic units are considered in the active power distribution network, the voltage distribution rule of the node voltage cannot be guaranteed to meet normal distribution. Therefore, the defects of large calculation amount or large calculation error cannot be avoided no matter a more accurate simulation method is adopted or an analytic method and an approximation method with certain limitations are selected.

Disclosure of Invention

In order to overcome the defects of the prior art, the invention provides a node equivalence-based active distribution network voltage out-of-limit risk analysis method, which fully considers the random characteristics of loads and distributed power supplies, performs analysis and calculation on the voltage out-of-limit probability of the active distribution network, performs power quality evaluation on the active distribution network in actual operation, and performs corresponding control according to the evaluation and analysis result.

In order to achieve the purpose of the invention, the invention adopts the following technical scheme:

the invention provides an active power distribution network voltage out-of-limit risk analysis method based on node equivalence, which comprises the following steps:

step 1: establishing a node equivalent load probability model, and establishing an equivalent state model of the active power distribution network by combining a photovoltaic system illumination intensity random model;

step 2: carrying out random load flow calculation on the discrete state of each equivalent node, and calculating the voltage out-of-limit probability of each equivalent node in the discrete state according to the random load flow result;

and step 3: and searching the adjacent values of the node equivalent state parameters in the actual running state of the node load in an offline database, and calculating the voltage out-of-limit probability in the actual running state of the node load.

The step 1 comprises the following steps:

step 1-1: selecting the maximum load state of each node in the active power distribution network, and establishing a node equivalent load probability model;

step 1-2: and establishing an equivalent state model of the active power distribution network by combining a random model of the illumination intensity of the photovoltaic system.

In the step 1-1, establishing a node equivalent load probability model includes:

assuming that the node h and the node k are any two adjacent nodes, the node h and the node k form a line hk, which has:

wherein,representing the vector of the voltage drop between node h and node k,representing the current vector, R, of the line hk_hkRepresenting the resistance, X, of the line hk_hkThe reactance of the line hk is shown,a vector of the potential of the node k is represented,represents the complex power flowing through node k;

neglecting the line loss, thenExpressed as:

wherein j is 1,2, …, N_k，N_kRepresenting the set of all nodes looking into the active distribution network from the head end of line hk behind node k,represents the load complex power of node j;

suppose thatRepresenting the rated voltage vector of the active distribution network, E_nRepresenting the magnitude of the rated voltage vector of the active distribution network, thusAnd is represented as:

wherein,to representThe conjugate of (a) to (b),represents the impedance vector of line hk;

therefore, for any equivalent node i in the active power distribution network, there are:

wherein,representing the vector of the voltage drop between the equivalent node i and the bus in the active distribution network, L_iRepresents the equivalent nodes i andall lines between the buses in the active power distribution network are aggregated,to representConjugation of (1);

if only the equivalent node i in the active power distribution network is loaded, the load is reducedAnd can be represented as:

wherein,representing the sum of the impedances between the equivalent node i and the busbars in the active distribution network,to representThe conjugate of (a) to (b),representing the complex power of the equivalent node i;

since the load power has random fluctuation, the active power short-term fluctuation and the reactive power short-term fluctuation of each node load both satisfy the normal distribution, and then are obtained by the following equations (5) and (6):

and has the following components:

wherein, a_hkTo representReal part of (b)_hkTo representAn imaginary part of (d); p_kRepresenting the sum of the active loads of all nodes following node k in the active distribution network, i.e.P_jRepresenting the active load of node j; q_kRepresenting the sum of the reactive loads of all nodes after node k in the active distribution network, i.e.Q_jRepresenting the reactive load of node j;

from the linear law of normal distribution then:

wherein, E (P)_eqi) Representing the equivalent active load expectation, E (Q), of the equivalent node i_eqi) Representing the equivalent reactive load expectation, P, of the equivalent node i_eqiRepresenting the equivalent active load, Q, of an equivalent node i_eqiRepresenting the equivalent reactive load of the equivalent node i, E (P)_j) Representing the active load expectation of node j, E (Q)_j) Represents the reactive load expectation of node j;

since equation (10) does not satisfy the random variable independence, it is transformed into:

and has the following components:

wherein N is_nodeRepresenting a set of load nodes in the active distribution network, m being 1,2, …, N_node；To representThe conjugate of (a) to (b),representing the complex power of the load node m; l is_mIndicates the line and L of the load node m_iWhen the intersection point which is closest to the load node m exists, all lines from the bus to the intersection point are collected; p_mRepresenting the active load, Q, of the load node m_mRepresenting the reactive load of the load node m; c. C_mAnd d_mRespectively representThe real and imaginary parts of (c);

thus, there are:

wherein, σ (P)_eqi) Represents the equivalent active load standard deviation, sigma (Q) of the equivalent node i_eqi) Represents the equivalent reactive load standard deviation, D (P) of the equivalent node i_eqi) Represents the equivalent active load variance, D (Q), of the equivalent node i_eqi) Represents the equivalent reactive load variance, D (P), of the equivalent node i_m) Representing the active load variance, D (Q), of the load node m_m) Representing the reactive load variance of load node m.

In the step 1-2, in the photovoltaic system illumination intensity random model, the solar illumination intensity obeys Beta distribution, and the solar illumination intensity is expected to be expressed by e(s), so that the active power distribution network equivalent state model is expressed as:

{E(S),E(P_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi)} (14)

wherein, σ (P)_eqi) Represents the equivalent active load standard deviation, sigma (Q) of the equivalent node i_eqi) Represents the equivalent reactive load standard deviation, E (P), of the equivalent node i_eqi) Representing the equivalent active load expectation, E (Q), of the equivalent node i_eqi) Representing the equivalent reactive load expectation of the equivalent node i.

The step 2 comprises the following steps:

step 2-1: selecting discrete states of equivalent nodes in the active power distribution network;

step 2-2: performing random load flow calculation on the discrete state of each equivalent node by adopting Latin hypercube sampling to obtain a random load flow result;

step 2-3: calculating the voltage out-of-limit probability of each equivalent node in a discrete state by adopting a majority theorem according to the random load flow result;

step 2-4: and storing the voltage out-of-limit probability of each equivalent node in a discrete state to an offline database.

The step 3 comprises the following steps:

step 3-1: acquiring the actual running state of each node load and the actual running state of the photovoltaic system;

step 3-2: searching an adjacent value of the node equivalent state parameter in an actual running state of the node load in an offline database;

step 3-3: and calculating the voltage out-of-limit probability of the node load in the actual running state by adopting a multidimensional Lagrange interpolation method, and analyzing the voltage out-of-limit risk.

In the step 3-2, the node equivalent state parameters include the solar illumination intensity expectation E (S), the equivalent active load expectation E (P) of the equivalent node i_eqi) And the equivalent active load standard deviation sigma (P) of the equivalent node i_eqi) Equivalent reactive load expectation E (Q) of equivalent node i_eqi) And the equivalent reactive load standard deviation sigma (Q) of the equivalent node i_eqi)。

The step 3-3 comprises the following steps:

step 3-3-1: calculating the voltage out-of-limit probability under the actual operation state of the node load by adopting a multidimensional Lagrange interpolation method, wherein the method comprises the following steps:

assume E (S), E (P)_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi) The downlink adjacent numbers found in the off-line database are respectively E⁰(S),E⁰(P_eqi),σ⁰(P_eqi),E⁰(Q_eqi),σ⁰(Q_eqi) The uplink adjacent numbers found in the offline database are respectively E¹(S),E¹(P_eqi),σ¹(P_eqi),E¹(Q_eqi),σ¹(Q_eqi) Then, the voltage out-of-limit probability f corresponding to the adjacent number is obtained, including:

wherein j is₁,j₂,...,j₅Respectively represent E (S), E (P)_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi) The values of the state index of (1) are both 0 or 1, namely:

j₁,j₂,...,j₅when the value of 0 is taken out,respectively represent E (S), E (P)_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi) The downlink adjacency number of (2);

j₁,j₂,...,j₅when the number 1 is taken out, the number 1,respectively represent E (S), E (P)_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi) The uplink adjacency number of (2);

by usingJ denotes E (S)₁An interpolation basis function, i.e. j₁When the value of 0 is taken out,0 th interpolation basis function l representing E (S)₀(E(S))；j₁When the number 1 is taken out, the number 1,1 st interpolation basis function l representing E (S)₁(E(S))；l₀(E (S)) and l₁(E (S)) are respectively represented as:

by usingRepresents E (P)_eqi) J (d) of₂An interpolation basis function, i.e. j₂When the value of 0 is taken out,represents E (P)_eqi) 0 th interpolation basis function l₀(E(P_eqi))；j₂When the number 1 is taken out, the number 1,represents E (P)_eqi) 1 st interpolation basis function l₁(E(P_eqi))；l₀(E(P_eqi) And l)₁(E(P_eqi) Respectively expressed as:

by usingRepresents sigma (P)_eqi) J (d) of₃An interpolation basis function, i.e. j₃When the value of 0 is taken out,represents sigma (P)_eqi) 0 th interpolation basis function l₀(σ(P_eqi))；j₃When the number 1 is taken out, the number 1,represents sigma (P)_eqi) 1 st interpolation basis function l₁(σ(P_eqi))；l₀(σ(P_eqi) And l)₁(σ(P_eqi) Respectively expressed as:

by usingRepresents E (Q)_eqi) J (d) of₄An interpolation basis function, i.e. j₄When the value of 0 is taken out,represents E (Q)_eqi) 0 th interpolation basis function l₀(E(Q_eqi))；j₄When the number 1 is taken out, the number 1,represents E (Q)_eqi) 1 st interpolation basis function l₁(E(Q_eqi))；l₀(E(Q_eqi) And l)₁(E(Q_eqi) Respectively expressed as:

by usingRepresents sigma (Q)_eqi) J (d) of₅An interpolation basis function, i.e. j₅When the value of 0 is taken out,represents sigma (Q)_eqi) 0 th interpolation basis function l₀(σ(Q_eqi))；j₅When the number 1 is taken out, the number 1,represents sigma (Q)_eqi) 1 st interpolation basis function l₁(σ(Q_eqi))；l₀(σ(Q_eqi) And l)₁(σ(Q_eqi) Respectively expressed as:

therefore, the voltage out-of-limit probability under the actual operation state of the node load is obtained by the following steps:

wherein f (E), (S), E (P)_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi) Represents the voltage out-of-limit probability under the actual operating state of the node load;

step 3-3-2: according to f (E), (S), E (P)_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi) Analysis of voltage out-of-limit risks, specifically: f (E), (S), E (P)_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi) The greater the voltage violation risk.

Compared with the closest prior art, the technical scheme provided by the invention has the following beneficial effects:

1) the method simplifies the running state parameters of the active power distribution network considering the load and the random characteristics of the photovoltaic system by using a node equivalent method, and represents the influence of the comprehensive action of the load of the whole system on the voltage of the node by using an equivalent load probability model of a single node;

2) the method has the advantages that the simplified characteristics that the quantity of equivalent state parameters of each node is small and the comprehensive influence effect of various running states of the system on the voltage of the node can be represented are utilized, the discrete state of each equivalent node in the active power distribution network can be selected according to the characteristics of the node to perform off-line calculation and generate a corresponding database, and a reference calculation sample is provided for on-line rapid analysis;

3) in the actual operation of the power distribution network, the random parameters of each node corresponding to the random parameters are calculated by using a node equivalence principle, namely, adjacent values can be searched in an offline database, a plurality of groups of discrete states are formed, so that the node voltage out-of-limit probability is obtained by performing rapid multidimensional Lagrange interpolation calculation, compared with a direct solving method which uses various random load flow methods and simultaneously considers a plurality of random variables, the method is more favorable for rapid online analysis and calculation and has higher accuracy;

4) the method effectively solves the problem of rapidly and accurately calculating the out-of-limit probability of each node voltage of the active power distribution network during actual operation.

Drawings

FIG. 1 is a flow chart of calculating out-of-limit voltage probability of each equivalent node in a discrete state by using a majority theorem according to an embodiment of the present invention;

FIG. 2 is a flowchart of calculating the out-of-limit voltage probability under the actual operating state of the node load by using a multidimensional Lagrange interpolation method according to the embodiment of the present invention.

Detailed Description

The present invention will be described in further detail with reference to the accompanying drawings.

The invention provides a node equivalence-based active power distribution network voltage out-of-limit risk analysis method, which adopts a method combining off-line calculation and on-line analysis to solve the problem of rapidly and accurately calculating out-of-limit probability of each node of a power distribution network during actual operation.

(1) The distribution system running state parameters considering the load and the random characteristics of the distributed power supply are simplified, so that the selection of a typical state in offline calculation and the mapping of an actual running state in online analysis are facilitated;

(2) according to the simplified running state parameters of the power distribution system, an offline typical state and voltage out-of-limit probability analysis result database is formed by selecting typical discrete states and performing immediate load flow calculation based on a simulation method, and a foundation is laid for quick calculation during online running;

(3) according to the node equivalence principle, the actual operation characteristics are equivalent to simplified operation parameters, adjacent values of the equivalent operation parameters are searched in an offline database, and finally the voltage out-of-limit probability in actual operation is rapidly calculated in a multi-dimensional interpolation mode.

The invention provides an active power distribution network voltage out-of-limit risk analysis method based on node equivalence, which comprises the following steps:

step 1: establishing a node equivalent load probability model, and establishing an equivalent state model of the active power distribution network by combining a photovoltaic system illumination intensity random model;

step 2: carrying out random load flow calculation on the discrete state of each equivalent node, and calculating the voltage out-of-limit probability of each equivalent node in the discrete state according to the random load flow result;

and step 3: and searching the adjacent values of the node equivalent state parameters in the actual running state of the node load in an offline database, and calculating the voltage out-of-limit probability in the actual running state of the node load.

The step 1 comprises the following steps:

step 1-1: selecting the maximum load state of each node in the active power distribution network, and establishing a node equivalent load probability model;

step 1-2: and establishing an equivalent state model of the active power distribution network by combining a random model of the illumination intensity of the photovoltaic system.

In the step 1-1, establishing a node equivalent load probability model includes:

assuming that the node h and the node k are any two adjacent nodes, the node h and the node k form a line hk, which has:

wherein,representing the vector of the voltage drop between node h and node k,representing the current vector, R, of the line hk_hkRepresenting the resistance, X, of the line hk_hkThe reactance of the line hk is shown,a vector of the potential of the node k is represented,represents the complex power flowing through node k;

neglecting the line loss, thenExpressed as:

wherein j is 1,2, …, N_k，N_kRepresenting the set of all nodes looking into the active distribution network from the head end of line hk behind node k,display sectionThe load complex power at point j;

suppose thatRepresenting the rated voltage vector of the active distribution network, E_nRepresenting the magnitude of the rated voltage vector of the active distribution network, thusAnd is represented as:

wherein,to representThe conjugate of (a) to (b),represents the impedance vector of line hk;

therefore, for any equivalent node i in the active power distribution network, there are:

wherein,representing the vector of the voltage drop between the equivalent node i and the bus in the active distribution network, L_iRepresenting the set of all lines between the equivalent node i and the bus in the active distribution network,to representConjugation of (1);

if only the equivalent node i in the active power distribution network is loaded, the load is reducedAnd can be represented as:

wherein,representing the sum of the impedances between the equivalent node i and the busbars in the active distribution network,to representThe conjugate of (a) to (b),representing the complex power of the equivalent node i;

since the load power has random fluctuation, the active power short-term fluctuation and the reactive power short-term fluctuation of each node load both satisfy the normal distribution, and then are obtained by the following equations (5) and (6):

and has the following components:

wherein, a_hkTo representReal part of (b)_hkTo representAn imaginary part of (d); p_kRepresenting the sum of the active loads of all nodes following node k in the active distribution network, i.e.P_jRepresenting the active load of node j; q_kRepresenting the sum of the reactive loads of all nodes after node k in the active distribution network, i.e.Q_jRepresenting the reactive load of node j;

from the linear law of normal distribution then:

wherein, E (P)_eqi) Representing the equivalent active load expectation, E (Q), of the equivalent node i_eqi) Representing the equivalent reactive load expectation, P, of the equivalent node i_eqiRepresenting the equivalent active load, Q, of an equivalent node i_eqiRepresenting the equivalent reactive load of the equivalent node i, E (P)_j) Representing the active load expectation of node j, E (Q)_j) Represents the reactive load expectation of node j;

since equation (10) does not satisfy the random variable independence, it is transformed into:

and has the following components:

wherein N is_nodeRepresenting a set of load nodes in the active distribution network, m being 1,2, …, N_node；To representThe conjugate of (a) to (b),representing the complex power of the load node m; l is_mIndicates the line and L of the load node m_iWhen the intersection point which is closest to the load node m exists, all lines from the bus to the intersection point are collected; p_mRepresenting the active load, Q, of the load node m_mRepresenting the reactive load of the load node m; c. C_mAnd d_mRespectively representThe real and imaginary parts of (c);

thus, there are:

wherein, σ (P)_eqi) Represents the equivalent active load standard deviation, sigma (Q) of the equivalent node i_eqi) Represents the equivalent reactive load standard deviation, D (P) of the equivalent node i_eqi) Represents the equivalent active load variance, D (Q), of the equivalent node i_eqi) Represents the equivalent reactive load variance, D (P), of the equivalent node i_m) Representing the active load variance, D (Q), of the load node m_m) Representing the reactive load variance of load node m.

In the step 1-2, in the photovoltaic system illumination intensity random model, the solar illumination intensity obeys Beta distribution, and the solar illumination intensity is expected to be expressed by e(s), so that the active power distribution network equivalent state model is expressed as:

{E(S),E(P_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi)} (14)

wherein, σ (P)_eqi) Represents the equivalent active load standard deviation, sigma (Q) of the equivalent node i_eqi) Represents the equivalent reactive load standard deviation, E (P), of the equivalent node i_eqi) Representing the equivalent active load expectation, E (Q), of the equivalent node i_eqi) Representing the equivalent reactive load expectation of the equivalent node i.

As shown in fig. 1, the step 2 includes the following steps:

step 2-1: selecting discrete states of equivalent nodes in the active power distribution network;

step 2-2: performing random load flow calculation on the discrete state of each equivalent node by adopting Latin hypercube sampling to obtain a random load flow result;

step 2-3: calculating the voltage out-of-limit probability of each equivalent node in a discrete state by adopting a majority theorem according to the random load flow result;

step 2-4: and storing the voltage out-of-limit probability of each equivalent node in a discrete state to an offline database.

As shown in fig. 2, the step 3 includes the following steps:

step 3-1: acquiring the actual running state of each node load and the actual running state of the photovoltaic system;

step 3-2: searching an adjacent value of the node equivalent state parameter in an actual running state of the node load in an offline database;

step 3-3: and calculating the voltage out-of-limit probability of the node load in the actual running state by adopting a multidimensional Lagrange interpolation method, and analyzing the voltage out-of-limit risk.

In the step 3-2, the node equivalent state parameters include the solar illumination intensity expectation E (S), the equivalent active load expectation E (P) of the equivalent node i_eqi) And the equivalent active load standard deviation sigma (P) of the equivalent node i_eqi) Equivalent reactive load expectation E (Q) of equivalent node i_eqi) And the equivalent reactive load standard deviation sigma (Q) of the equivalent node i_eqi)。

The step 3-3 comprises the following steps:

step 3-3-1: calculating the voltage out-of-limit probability under the actual operation state of the node load by adopting a multidimensional Lagrange interpolation method, wherein the method comprises the following steps:

assume E (S), E (P)_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi) The downlink adjacent numbers found in the off-line database are respectively E⁰(S),E⁰(P_eqi),σ⁰(P_eqi),E⁰(Q_eqi),σ⁰(Q_eqi) The uplink adjacent numbers found in the offline database are respectively E¹(S),E¹(P_eqi),σ¹(P_eqi),E¹(Q_eqi),σ¹(Q_eqi) Then, the voltage out-of-limit probability f corresponding to the adjacent number is obtained, including:

wherein j is₁,j₂,...,j₅Respectively represent E (S), E (P)_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi) The values of the state index of (1) are both 0 or 1, namely:

j₁,j₂,...,j₅when the value of 0 is taken out,respectively represent E (S), E (P)_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi) The downlink adjacency number of (2);

j₁,j₂,...,j₅when the number 1 is taken out, the number 1,respectively represent E (S), E (P)_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi) The uplink adjacency number of (2);

by usingJ denotes E (S)₁An interpolation basis function, i.e. j₁When the value of 0 is taken out,0 th interpolation basis function l representing E (S)₀(E(S))；j₁When the number 1 is taken out, the number 1,1 st interpolation basis function l representing E (S)₁(E(S))；l₀(E (S)) and l₁(E (S)) are respectively represented as:

by usingRepresents E (P)_eqi) J (d) of₂An interpolation basis function, i.e. j₂When the value of 0 is taken out,represents E (P)_eqi) 0 th interpolation basis function l₀(E(P_eqi))；j₂When the number 1 is taken out, the number 1,represents E (P)_eqi) 1 st interpolation basis function l₁(E(P_eqi))；l₀(E(P_eqi) And l)₁(E(P_eqi) Respectively expressed as:

by usingRepresents sigma (P)_eqi) J (d) of₃An interpolation basis function, i.e. j₃When the value of 0 is taken out,represents sigma (P)_eqi) 0 th interpolation basis function l₀(σ(P_eqi))；j₃When the number 1 is taken out, the number 1,represents sigma (P)_eqi) 1 st interpolation basis function l₁(σ(P_eqi))；l₀(σ(P_eqi) And l)₁(σ(P_eqi) Respectively expressed as:

by usingRepresents E (Q)_eqi) J (d) of₄An interpolation basis function, i.e. j₄When the value of 0 is taken out,represents E (Q)_eqi) 0 th interpolation basis function l₀(E(Q_eqi))；j₄When the number 1 is taken out, the number 1,represents E (Q)_eqi) 1 st interpolation basis function l₁(E(Q_eqi))；l₀(E(Q_eqi) And l)₁(E(Q_eqi) Respectively expressed as:

by usingRepresents sigma (Q)_eqi) J (d) of₅An interpolation basis function, i.e. j₅When the value of 0 is taken out,represents sigma (Q)_eqi) 0 th interpolation basis function l₀(σ(Q_eqi))；j₅When the number 1 is taken out, the number 1,represents sigma (Q)_eqi) 1 st interpolation basis function l₁(σ(Q_eqi))；l₀(σ(Q_eqi) And l)₁(σ(Q_eqi) Respectively expressed as:

therefore, the voltage out-of-limit probability under the actual operation state of the node load is obtained by the following steps:

wherein f (E), (S), E (P)_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi) Represents the voltage out-of-limit probability under the actual operating state of the node load;

step 3-3-2: according to f (E), (S), E (P)_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi) Analysis of voltage out-of-limit risks, specifically: f (E), (S), E (P)_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi) The greater the voltage violation risk.

Finally, it should be noted that: the above embodiments are only intended to illustrate the technical solution of the present invention and not to limit the same, and a person of ordinary skill in the art can make modifications or equivalents to the specific embodiments of the present invention with reference to the above embodiments, and such modifications or equivalents without departing from the spirit and scope of the present invention are within the scope of the claims of the present invention as set forth in the claims.

Claims (8)

1. An active power distribution network voltage out-of-limit risk analysis method based on node equivalence is characterized by comprising the following steps: the analysis method comprises the following steps:

step 1: establishing a node equivalent load probability model, and establishing an equivalent state model of the active power distribution network by combining a photovoltaic system illumination intensity random model;

step 2: carrying out random load flow calculation on the discrete state of each equivalent node, and calculating the voltage out-of-limit probability of each equivalent node in the discrete state according to the random load flow result;

and step 3: and searching the adjacent values of the node equivalent state parameters in the actual running state of the node load in an offline database, and calculating the voltage out-of-limit probability in the actual running state of the node load.

2. The node equivalence-based active distribution network voltage out-of-limit risk analysis method according to claim 1, characterized in that: the step 1 comprises the following steps:

step 1-1: selecting the maximum load state of each node in the active power distribution network, and establishing a node equivalent load probability model;

step 1-2: and establishing an equivalent state model of the active power distribution network by combining a random model of the illumination intensity of the photovoltaic system.

3. The node equivalence-based active distribution network voltage out-of-limit risk analysis method according to claim 2, characterized in that: in the step 1-1, establishing a node equivalent load probability model includes:

assuming that the node h and the node k are any two adjacent nodes, the node h and the node k form a line hk, which has:

${\stackrel{\·}{V}}_{hk}={\stackrel{\·}{I}}_{hk}(R_{hk}+{\mathrm{jX}}_{hk})={\left(\frac{{\stackrel{\‾}{S}}_k}{{\stackrel{\·}{E}}_k}\right)}^{*}(R_{hk}+{\mathrm{jX}}_{hk})---\left(1\right)$

wherein,representing the vector of the voltage drop between node h and node k,representing the current vector, R, of the line hk_hkRepresenting the resistance, X, of the line hk_hkThe reactance of the line hk is shown,a vector of the potential of the node k is represented,represents the complex power flowing through node k;

neglecting the line loss, thenExpressed as:

${\stackrel{\‾}{S}}_k=\underset{j\∈N_k}{\Σ}{\stackrel{\‾}{S}}_j---\left(2\right)$

wherein j is 1,2, …, N_k，N_kRepresenting the set of all nodes looking into the active distribution network from the head end of line hk behind node k,represents the load complex power of node j;

suppose that Representing the rated voltage vector of the active distribution network, E_nRepresenting the magnitude of the rated voltage vector of the active distribution network, thusAnd is represented as:

${\stackrel{\·}{V}}_{hk}=\frac{1}{E_n}{\stackrel{\‾}{S}}_k^{*}{\stackrel{\·}{Z}}_{hk}=\frac{{\stackrel{\‾}{S}}_k^{*}}{E_n}(R_{hk}+{\mathrm{jX}}_{hk})---\left(3\right)$

wherein,to representThe conjugate of (a) to (b),represents the impedance vector of line hk;

therefore, for any equivalent node i in the active power distribution network, there are:

${\stackrel{\·}{V}}_{0i}=\underset{hk\∈L_i}{\Σ}{\stackrel{\·}{V}}_{hk}=\underset{hk\∈L_i}{\Σ}\[\frac{{\stackrel{\·}{Z}}_{hk}}{E_n}\left(\underset{j\∈N_k}{\Σ}{\stackrel{\‾}{S}}_j^{*}\right)\]---\left(4\right)$

wherein,representing the vector of the voltage drop between the equivalent node i and the bus in the active distribution network, L_iRepresenting the set of all lines between the equivalent node i and the bus in the active distribution network,to representConjugation of (1);

if only the equivalent node i in the active power distribution network is loaded, the load is reducedAnd can be represented as:

${\stackrel{\·}{V}}_{0i}=\frac{{\stackrel{\·}{Z}}_{0i}{\stackrel{\‾}{S}}_{eqi}^{*}}{E_n}---\left(5\right)$

wherein,representing the sum of the impedances between the equivalent node i and the busbars in the active distribution network,to representThe conjugate of (a) to (b),representing the complex power of the equivalent node i;

since the load power has random fluctuation, the active power short-term fluctuation and the reactive power short-term fluctuation of each node load both satisfy the normal distribution, and then are obtained by the following equations (5) and (6):

${\stackrel{\‾}{S}}_{eqi}^{*}=\underset{hk\∈L_i}{\Σ}\[\frac{{\stackrel{\·}{Z}}_{hk}}{{\stackrel{\·}{Z}}_{0i}}\left(\underset{j\∈N_k}{\Σ}{\stackrel{\‾}{S}}_j^{*}\right)\]=\underset{hk\∈L_i}{\Σ}\[(a_{hk}{P}_k+b_{hk}{Q}_k)+j(b_{hk}{P}_k-a_{hk}{Q}_k)\]---\left(6\right)$

and has the following components:

$\frac{{\stackrel{\·}{Z}}_{hk}}{{\stackrel{\·}{Z}}_{0i}}=a_{hk}+{\mathrm{jb}}_{hk}---\left(7\right)$

wherein, a_hkTo representThe real part of (a) is,b_hkto representAn imaginary part of (d); p_kRepresenting the sum of the active loads of all nodes following node k in the active distribution network, i.e.P_jRepresenting the active load of node j; q_kRepresenting the sum of the reactive loads of all nodes after node k in the active distribution network, i.e.Q_jRepresenting the reactive load of node j;

from the linear law of normal distribution then:

$E\left(P_{eqi}\right)=\underset{hk\∈L_i}{\Σ}\[a_{hk}\underset{j\∈N_k}{\Σ}E\left(P_j\right)+b_{hk}\underset{j\∈N_k}{\Σ}E\left(Q_j\right)\]---\left(8\right)$

$E\left(Q_{eqi}\right)=\underset{hk\∈L_i}{\Σ}\[a_{hk}\underset{j\∈N_k}{\Σ}E\left(Q_j\right)-b_{hk}\underset{j\∈N_k}{\Σ}E\left(P_j\right)\]---\left(9\right)$

wherein, E (P)_eqi) Representing the equivalent active load expectation, E (Q), of the equivalent node i_eqi) Representing the equivalent reactive load expectation, P, of the equivalent node i_eqiRepresenting the equivalent active load, Q, of an equivalent node i_eqiRepresenting the equivalent reactive load of the equivalent node i, E (P)_j) Representing the active load expectation of node j, E (Q)_j) Represents the reactive load expectation of node j;

since equation (10) does not satisfy the random variable independence, it is transformed into:

${\stackrel{\‾}{S}}_{eqi}^{*}=\frac{\underset{m\∈N_{node}}{\Σ}\[{\stackrel{\‾}{S}}_m^{*}\underset{hk\∈L_m}{\Σ}{\stackrel{\·}{Z}}_{hk}\]}{{\stackrel{\·}{Z}}_{0i}}=\underset{m\∈N_{node}}{\Σ}\[\left(c_m{P}_m+d_m{Q}_m\right)+j\left(d_m{P}_m-c_m{Q}_m\right)\]---\left(10\right)$

and has the following components:

$\frac{\underset{hk\∈L_m}{\Σ}{\stackrel{\·}{Z}}_{hk}}{{\stackrel{\·}{Z}}_{0i}}=c_m+{\mathrm{jd}}_m---\left(11\right)$

wherein N is_nodeRepresenting a set of load nodes in the active distribution network, m being 1,2, …, N_node；To representThe conjugate of (a) to (b),representing the complex power of the load node m; l is_mIndicates the line and L of the load node m_iWhen the intersection point which is closest to the load node m exists, all lines from the bus to the intersection point are collected; p_mRepresenting the active load, Q, of the load node m_mRepresenting the reactive load of the load node m; c. C_mAnd d_mRespectively representThe real and imaginary parts of (c);

thus, there are:

$\mathrm{\σ}\left(P_{eqi}\right)=\sqrt{D\left(P_{eqi}\right)}=\sqrt{\underset{m\∈N_{node}}{\Σ}\[c_m^{2}D\left(P_m\right)+d_m^{2}D\left(Q_m\right)\]}---\left(12\right)$

$\mathrm{\σ}\left(Q_{eqi}\right)=\sqrt{D\left(Q_{eqi}\right)}=\sqrt{\underset{m\∈N_{node}}{\Σ}\[d_m^{2}D\left(P_m\right)+c_m^{2}D\left(Q_m\right)\]}---\left(13\right)$

wherein, σ (P)_eqi) Represents the equivalent active load standard deviation, sigma (Q) of the equivalent node i_eqi) Represents the equivalent reactive load standard deviation, D (P) of the equivalent node i_eqi) Represents the equivalent active load variance, D (Q), of the equivalent node i_eqi) Represents the equivalent reactive load variance, D (P), of the equivalent node i_m) Representing the active load variance, D (Q), of the load node m_m) Representing the reactive load variance of load node m.

4. The node equivalence-based active distribution network voltage out-of-limit risk analysis method according to claim 3, wherein: in the step 1-2, in the photovoltaic system illumination intensity random model, the solar illumination intensity obeys Beta distribution, and the solar illumination intensity is expected to be expressed by e(s), so that the active power distribution network equivalent state model is expressed as:

{E(S),E(P_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi)} (14)

wherein, σ (P)_eqi) Represents the equivalent active load standard deviation, sigma (Q) of the equivalent node i_eqi) Represents the equivalent reactive load standard deviation, E (P), of the equivalent node i_eqi) Representing the equivalent active load expectation, E (Q), of the equivalent node i_eqi) Representing the equivalent reactive load expectation of the equivalent node i.

5. The node equivalence-based active distribution network voltage out-of-limit risk analysis method according to claim 1, characterized in that: the step 2 comprises the following steps:

step 2-1: selecting discrete states of equivalent nodes in the active power distribution network;

step 2-2: performing random load flow calculation on the discrete state of each equivalent node by adopting Latin hypercube sampling to obtain a random load flow result;

step 2-3: calculating the voltage out-of-limit probability of each equivalent node in a discrete state by adopting a majority theorem according to the random load flow result;

step 2-4: and storing the voltage out-of-limit probability of each equivalent node in a discrete state to an offline database.

6. The node equivalence-based active distribution network voltage out-of-limit risk analysis method according to claim 1, characterized in that: the step 3 comprises the following steps:

step 3-1: acquiring the actual running state of each node load and the actual running state of the photovoltaic system;

step 3-2: searching an adjacent value of the node equivalent state parameter in an actual running state of the node load in an offline database;

step 3-3: and calculating the voltage out-of-limit probability of the node load in the actual running state by adopting a multidimensional Lagrange interpolation method, and analyzing the voltage out-of-limit risk.

7. The node equivalence-based active distribution network voltage out-of-limit risk analysis method according to claim 6, wherein: in the step 3-2, the node equivalent state parameters include the solar illumination intensity expectation E (S), the equivalent active load expectation E (P) of the equivalent node i_eqi) And the equivalent active load standard deviation sigma (P) of the equivalent node i_eqi) Equivalent reactive load expectation E (Q) of equivalent node i_eqi) And the equivalent reactive load standard deviation sigma (Q) of the equivalent node i_eqi)。

8. The node equivalence-based active distribution network voltage out-of-limit risk analysis method according to claim 7, wherein: the step 3-3 comprises the following steps:

step 3-3-1: calculating the voltage out-of-limit probability under the actual operation state of the node load by adopting a multidimensional Lagrange interpolation method, wherein the method comprises the following steps:

assume E (S), E (P)_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi) The downlink adjacent numbers found in the off-line database are respectively E⁰(S),E⁰(P_eqi),σ⁰(P_eqi),E⁰(Q_eqi),σ⁰(Q_eqi) In an off-line databaseThe found uplink adjacent numbers are respectively E¹(S),E¹(P_eqi),σ¹(P_eqi),E¹(Q_eqi),σ¹(Q_eqi) Then, the voltage out-of-limit probability f corresponding to the adjacent number is obtained, including:

$f=f\left(E^{j_1}\right(S),E^{j_2}(P_{eqi}),{\mathrm{\σ}}^{j_3}(P_{eqi}),E^{j_4}(Q_{eqi}),{\mathrm{\σ}}^{j_5}(Q_{eqi}\left)\right)---\left(15\right)$

wherein j is₁,j₂,...,j₅Respectively represent E (S), E (P)_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi) The values of the state index of (1) are both 0 or 1, namely:

j₁,j₂,...,j₅when the value of 0 is taken out,respectively represent E (S), E (P)_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi) The downlink adjacency number of (2);

j₁,j₂,...,j₅when the number 1 is taken out, the number 1,respectively represent E (S), E (P)_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi) The uplink adjacency number of (2);

by usingJ denotes E (S)₁An interpolation basis function, i.e. j₁When the value of 0 is taken out,0 th interpolation basis function l representing E (S)₀(E(S))；j₁When the number 1 is taken out, the number 1,1 st interpolation basis function l representing E (S)₁(E(S))；l₀(E (S)) and l₁(E (S)) are respectively represented as:

$l_0\left(E\right(S\left)\right)=\frac{E\left(S\right)-E^1\left(S\right)}{E^0\left(S\right)-E^1\left(S\right)}---\left(16\right)$

$l_1\left(E\right(S\left)\right)=\frac{E\left(S\right)-E^0\left(S\right)}{E^1\left(S\right)-E^0\left(S\right)}---\left(17\right)$

by usingRepresents E (P)_eqi) J (d) of₂An interpolation basis function, i.e. j₂When the value of 0 is taken out,represents E (P)_eqi) 0 th interpolation basis function l₀(E(P_eqi))；j₂When the number 1 is taken out, the number 1,represents E (P)_eqi) 1 st interpolation basis function l₁(E(P_eqi))；l₀(E(P_eqi) And l)₁(E(P_eqi) Respectively expressed as:

$l_0\left(E\right(P_{eqi}\left)\right)=\frac{E\left(P_{eqi}\right)-E^1\left(P_{eqi}\right)}{E^0\left(P_{eqi}\right)-E^1\left(P_{eqi}\right)}---\left(18\right)$

$l_1\left(E\right(P_{eqi}\left)\right)=\frac{E\left(P_{eqi}\right)-E^0\left(P_{eqi}\right)}{E^1\left(P_{eqi}\right)-E^0\left(P_{eqi}\right)}---\left(19\right)$

by usingRepresents sigma (P)_eqi) J (d) of₃An interpolation basis function, i.e. j₃When the value of 0 is taken out,represents sigma (P)_eqi) 0 th interpolation basis function l₀(σ(P_eqi))；j₃When the number 1 is taken out, the number 1,represents sigma (P)_eqi) 1 st interpolation basis function l₁(σ(P_eqi))；l₀(σ(P_eqi) And l)₁(σ(P_eqi) Respectively expressed as:

$l_0\left(\mathrm{\σ}\right(P_{eqi}\left)\right)=\frac{\mathrm{\σ}\left(P_{eqi}\right)-{\mathrm{\σ}}^1\left(P_{eqi}\right)}{{\mathrm{\σ}}^0\left(P_{eqi}\right)-{\mathrm{\σ}}^1\left(P_{eqi}\right)}---\left(20\right)$

$l_1\left(\mathrm{\σ}\right(P_{eqi}\left)\right)=\frac{\mathrm{\σ}\left(P_{eqi}\right)-{\mathrm{\σ}}^0\left(P_{eqi}\right)}{{\mathrm{\σ}}^1\left(P_{eqi}\right)-{\mathrm{\σ}}^0\left(P_{eqi}\right)}---\left(21\right)$

by usingRepresents E (Q)_eqi) J (d) of₄An interpolation basis function, i.e. j₄When the value of 0 is taken out,represents E (Q)_eqi) 0 th interpolation basis function l₀(E(Q_eqi))；j₄When the number 1 is taken out, the number 1,represents E (Q)_eqi) 1 st interpolation basis function l₁(E(Q_eqi))；l₀(E(Q_eqi) And l)₁(E(Q_eqi) Respectively expressed as:

$l_0\left(E\right(Q_{eqi}\left)\right)=\frac{E\left(Q_{eqi}\right)-E^1\left(Q_{eqi}\right)}{E^0\left(Q_{eqi}\right)-E^1\left(Q_{eqi}\right)}---\left(22\right)$

$l_1\left(E\right(Q_{eqi}\left)\right)=\frac{E\left(Q_{eqi}\right)-E^0\left(Q_{eqi}\right)}{E^1\left(Q_{eqi}\right)-E^0\left(Q_{eqi}\right)}---\left(23\right)$

by usingRepresents sigma (Q)_eqi) J (d) of₅An interpolation basis function, i.e. j₅When the value of 0 is taken out,represents sigma (Q)_eqi) 0 th interpolation basis function l₀(σ(Q_eqi))；j₅When the number 1 is taken out, the number 1,represents sigma (Q)_eqi) 1 st interpolation basis function l₁(σ(Q_eqi))；l₀(σ(Q_eqi) And l)₁(σ(Q_eqi) Respectively expressed as:

$l_0\left(\mathrm{\σ}\right(Q_{eqi}\left)\right)=\frac{\mathrm{\σ}\left(Q_{eqi}\right)-{\mathrm{\σ}}^1\left(Q_{eqi}\right)}{{\mathrm{\σ}}^0\left(Q_{eqi}\right)-{\mathrm{\σ}}^1\left(Q_{eqi}\right)}---\left(24\right)$

$l_1\left(\mathrm{\σ}\right(Q_{eqi}\left)\right)=\frac{\mathrm{\σ}\left(Q_{eqi}\right)-{\mathrm{\σ}}^0\left(Q_{eqi}\right)}{{\mathrm{\σ}}^1\left(Q_{eqi}\right)-{\mathrm{\σ}}^0\left(Q_{eqi}\right)}---\left(25\right)$

therefore, the voltage out-of-limit probability under the actual operation state of the node load is obtained by the following steps:

$\begin{array}{c}f\left(E\left(S\right),E\left(P_{eqi}\right),\mathrm{\σ}\left(P_{eqi}\right),E\left(Q_{eqi}\right),\mathrm{\σ}\left(Q_{eqi}\right)\right)=\\ \underset{j_1=0}{\overset{1}{\Σ}}\underset{j_2=0}{\overset{1}{\Σ}}...\underset{j_5=0}{\overset{1}{\Σ}}\left[\begin{array}{c}{l}_{j_1}\left(E\left(S\right)\right)\×l_{j_2}\left(E\left(P_{eqi}\right)\right)\×l_{j_3}\left(\mathrm{\σ}\left(P_{eqi}\right)\right)\×l_{j_4}\left(E\left(Q_{eqi}\right)\right)\×l_{j_5}\left(\mathrm{\σ}\left(Q_{eqi}\right)\right)\\ \×f\left(E^{j_1}\left(S\right),E^{j_2}\left(P_{eqi}\right),{\mathrm{\σ}}^{j_3}\left(P_{eqi}\right),E^{j_4}\left(Q_{eqi}\right),{\mathrm{\σ}}^{j_5}\left(Q_{eqi}\right)\right)\end{array}\right]\end{array}---\left(26\right)$

wherein f (E), (S), E (P)_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi) Represents the voltage out-of-limit probability under the actual operating state of the node load;

step 3-3-2: according to f (E), (S), E (P)_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi) Analysis of voltage out-of-limit risks, specifically: f (E), (S), E (P)_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi) The greater the voltage violation risk.